There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 4cos(4x) - 16cos(2x) + 12 - 32{(sin(x))}^{4}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 4cos(4x) - 16cos(2x) - 32sin^{4}(x) + 12\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 4cos(4x) - 16cos(2x) - 32sin^{4}(x) + 12\right)}{dx}\\=&4*-sin(4x)*4 - 16*-sin(2x)*2 - 32*4sin^{3}(x)cos(x) + 0\\=& - 128sin^{3}(x)cos(x) + 32sin(2x) - 16sin(4x)\\ \end{split}\end{equation} \]

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